A uniform string is stretched along the x-axis. Two transverse sinusoidal waves, Wave A and Wave B, travel simultaneously along the string toward increasing x. Both waves have the same amplitude, frequency, and wavelength. At time t=0, the displacement of the string at the origin is observed to be
• zero and increasing upward for Wave A, and
• zero and decreasing downward for Wave B.
Assume the positive y direction is upward.
(a) Describe qualitatively how the two waves differ in their displacement–versus–time graphs at the origin during the first half-period after t=0. Reference the relative timing of crests and troughs in your explanation.
(b) The mathematical representation of a traveling sinusoidal wave contains a phase constant. Explain, without performing explicit calculations, why the sign of the phase constant must differ between Wave A and Wave B in order to reproduce the observed initial motions at the origin.
(c) Using complete sentences, discuss how a change in phase constant affects the appearance of a snapshot graph y versus x taken at a fixed instant of time. Include specific reference to the location of nodes, crests, and troughs.